limits to bank deposit market power
TRANSCRIPT
Limits to Bank Deposit Market Power Juliane Begenau Erik Stafford
Working Paper 22-039
Working Paper 22-039
Copyright © 2021 by Juliane Begenau and Erik Stafford.
Working papers are in draft form. This working paper is distributed for purposes of comment and discussion only. It may not be reproduced without permission of the copyright holder. Copies of working papers are available from the author.
Funding for this research was provided in part by Harvard Business School.
Limits to Bank Deposit Market Power Juliane Begenau Stanford University
Erik Stafford Harvard Business School
Limits to Bank Deposit Market Power*
Juliane Begenau† Erik Stafford ‡
November 2021
Abstract
Claims about the market power of bank deposits in the banking literature are numerousand far reaching. Recently, a causal narrative has emerged in the banking literature: marketpower in bank deposits, measured as imperfect pass-through of short-term market rates ondeposit rates, allows banks to eliminate their asset interest rate exposure and to achieve nearconstant net interest margin (NIM). We show that the empirical evidence does not support theseconclusions. We show that neither deposits nor market power are essential for achieving stableNIM in long-short fixed income portfolios. We show that matching interest income and interestexpenses sensitivities to market rate movements is a consequence of achieving stable NIM,not necessarily the mechanism that allows it. Stable NIM does not imply near zero interestrate risk according to standard risk measures. Common measures of imperfect pass-throughof market rates to bank deposit rates commingle two distinct mechanisms: (1) intentionalrate setting and (2) mechanical consequence of comparing the changes in the periodic interestearned on positive maturity fixed coupon portfolios to changes in a short-term interest rate. Themechanical maturity consequence dominates the measured imperfect pass-through of marketrates on time deposits.
*We thank Darrell Duffie, Mark Egan, Samuel Hanson, Victoria Ivashina, Hanno Lustig, Arvind Krishnamurthy,Teodora Paligorova, Amit Seru, Adi Sunderam, and seminar participants at the Federal Reserve Board, the FRBNew York, Harvard Business School, Princeton, Stanford GSB, and the 4th Bank of Canada FSRC Macro-FinanceConference for helpful comments and discussions.
†Begenau: Stanford GSB and NBER and CEPR. E-mail: [email protected]‡Stafford: HBS. E-mail: [email protected]
1 Introduction
Claims about the market power of bank deposits in the banking literature are numerous and far
reaching. The literature has associated bank market power with the transmission of monetary
policy,1 relationship banking,2 and banks’ interest rate risk exposure.3 Our focus is on recent
claims that deposit market power allows banks to eliminate their interest rate risk exposure. This
conclusion is consequential for assessing the overall performance of banks since a maturity term
risk premium is one of the best performing risk premia available to US investors over the past
forty years.4 A traditional view of banks that has banks bearing several units of this risk premium
through their high leverage and the maturity mismatch between their assets and liabilities is quite
different from the recent view of near 0 units of this risk premium. This striking difference in
views can generate an economically large benchmark performance difference. The quantity of net
interest rate risk exposure in banks is also relevant for assessing overall stability of the banking
sector. The Federal Reserve and FDIC researchers viewed the large interest rate increases in the
US around 1980 as instrumental in creating an incentive for many banks to gamble their way out of
their effective insolvency, created by the large gap between the accounting values and the market
values of bank asset portfolios, through high risk loan origination that materialized as losses years
later (Federal Reserve, 2013; FDIC, 1997).
This paper reexamines the evidence to reach recent conclusions that (a) banks bear no interest
rate risk; (b) market power and the deposits-taking activity are instrumental in allowing for asset
and liability spread beta matching, which in turn allows banks to achieve stable net interest margin;
and (c) the robustness of the imperfect pass-through of deposit rates as a measure of deposit market
power. Our findings show that these conclusions are not robustly supported by the data.
Three empirical properties of bank income and expense rates, summarized in Figure 1, form the
recent narrative that banks have used their deposit market power to intentionally hedge their interest
1E.g., Drechsler, Savov, and Schnabl (2017); Wang (2018); Wang, Whited, Wu, and Xiao (Forthcoming)2E.g., Granja, Leuz, and Rajan (2018)3E.g., Hoffmann, Langfield, Pierobon, and Vuillemey (2019); Drechsler, Savov, and Schnabl (2021)4A 5-year US Treasury term factor has earned an annualized return of 7.3% over our sample period, 1995 to 2020.
1
rate risk exposure, achieving stable net interest margin and no net interest rate risk. First, banks
pay interest rates on their deposits that do not reflect current market conditions as the top panel in
Figure 1 illustrates. In periods of increasing short-term interest rates, deposit rates increase at a
substantially slower rate, which suggests imperfect pass-through of market rates to deposit rates.5
Additionally, bank deposit rates are generally below the short-term market rate. In conjunction with
the assumption that banks with different pass-through rates face identical incremental operating
costs, this failure of marginal cost pricing suggests that banks have substantial deposit market
power.
Second, in a series of influential papers, Drechsler, Savov, and Schnabl (2017, 2021) document
a strong pattern of asset (interest income) and liability (interest expense) spread beta matching in
the cross section of US commercial banks, illustrated in the middle panel in Figure 1. The spread
beta of bank deposits is statistically equivalent to the imperfect pass-through coefficient of the
earlier literature. Both are estimated from the same regression of the difference between a short-
term market interest rate, say the Federal funds rate (FFR), and the interest paid on bank deposits,
on changes in the short-term market interest rate. The relabelling of the pass-through coefficient
to spread beta connotes a risk measure that suggests banks have hedged their asset risk by having
equivalently risky liabilities.
The strong empirical relation of asset and liability spread beta matching forms the basis for
interpreting the third empirical regularity. Banks have highly stable net interest margins (NIM), as
illustrated in the bottom panel of Figure 1.6 The NIM of the aggregate banking sector is remarkably
stable through time, fluctuating substantially less than the short-term market interest rate, proxied
here by the FFR. At the individual bank level, NIM is also stable through time. The average time
series standard deviation of the quarterly change in NIM for all US commercial banks is 0.15%,
with the 95th percentile equaling 0.27%, while the standard deviation of the quarterly change in the
FFR is 0.70%. Viewing the spread betas as risk measures, Drechsler, Savov, and Schnabl (2021) are
5Early papers in the empirical literature examining the relation between deposit rates and market interest ratesinclude Ausubel (1992); Berger and Hannan (1989); Diebold and Sharpe (1990); Hannan and Liang (1993); Hannanand Berger (1997); Neumark and Sharpe (1992); Driscoll and Judson (2013).
6NIM is defined as interest income minus interest expense, scaled by book assets.
2
able to interpret the stable NIM as evidence of banks engaging in maturity transformation without
bearing interest rate risk, enabled by the market power derived from their deposit franchise.7
We examine the joint interpretation of the three basic properties illustrated in Figure 1 to assess
how well-identified are the conclusions in the literature. We begin with two basic observations.
First, as long as NIM is stable, banks’ interest income and interest expense betas must match.
Consider Y = A−B, to represent NIM equaling an interest income rate minus an interest expense
rate. In the limit of zero variance of Y , any random variable, X , that is correlated with A must be
identically correlated with B. For example, the income and expense betas from a regression of bank
income and bank expense on the quarterly returns of Amazon stock will match as well. Hence,
asset and liability spread beta matching is a consequence of banks achieving nearly constant NIM.
As such, it cannot cleanly identify the mechanism that leads to constant NIM. This is important
because it means that asset and liability spread matching represents a transformation of the known
fact that banks have stable NIM, not an additional piece of evidence to support a causal narrative.
Second, interest income and interest expense betas are incomplete measures of interest rate risk
relative to the standard measures used in textbooks (Berk and DeMarzo, 2019; Cochrane, 2009),
used by bond investors, and in the asset pricing literature (e.g., Fama and French, 1989); and
therefore the fact that they offset at the bank level conveys little about a bank’s actual exposure to
interest rate risk. Interest spread betas measure the sensitivity of portfolio income and expense to
interest rate changes (i.e. coupon payments), while traditional interest rate risk measures quantify
the sensitivity of portfolio value to interest rate changes. This important distinction allows for the
possibility that substantial interest rate risk resides in portfolios that appears to have none according
to income based metrics.
We propose two tests of the causal narrative. First, if "two essential properties of the deposit
franchise drive this result" (market power and fixed non-interest costs of deposits)8 then a price
7Other recent papers relying on net interest income fluctuations as a measure of interest rate risk exposure includeHoffmann et al. (2019); Jiang and Zhang (2021); Gomez et al. (2021).
8Drechsler, Savov, and Schnabl (2021) state, "In this paper we show that despite having a large maturity mismatchbanks do not take on significant interest rate risk. Rather, because of the deposit franchise, maturity transformationactually reduces the amount of interest rate risk banks take on. Two essential properties of the deposit franchise drivethis result. First, the deposit franchise gives banks market power over retail deposits, which allows them to borrow
3
taking long-short portfolio strategy in US Treasuries cannot achieve a stable NIM. Second, in a
cross section of price-taking portfolio strategies that achieve stable NIM and that produce matching
(i.e. offsetting) income and expense betas, the interest rate exposure of these portfolios will be zero.
We can reject both of these hypotheses.
We design various long-short portfolios of US Treasury securities that are as successful as
banks in generating constant NIM despite operating under a number of constraints. These portfo-
lios have neither banks’ price-setting power over loans and deposits nor banks’ range of investment
and funding options at their disposals. These results reject the notion that market power and bank
deposits are necessary for achieving stable NIM.
Additionally, we examine the asset and liability spread betas of these US Treasury portfolios
that achieve stable NIM and find a strong pattern of asset and liability beta matching. Because
these stable NIM UST portfolios are designed to have positive mean NIM targets, they have pos-
itive maturity mismatches between their assets and liabilities. Consistent with basic fixed income
valuation, we find that there is a very tight link between the maturity mismatch and both model-
implied duration risk exposure and regression based duration risk exposure estimates. In other
words, these portfolios carry substantial interest rate risk exposures while also featuring near con-
stant NIMs and matching asset and liability betas. These results reject the notion that portfolios
achieving constant NIM combined with asset and liability spread beta matching imply near zero
interest rate exposure.
While our UST portfolios are not designed to mimic banks’ portfolios, this analysis clarifies
that the existing evidence is uninformative about banks’ interest rate risk exposure. It also casts
doubt on using spread betas or imperfect pass-through coefficients as a measure of bank deposit
market power. Specifically, passive US Treasury portfolios with positive maturity, which clearly
do not have market power, exhibit substantial imperfect pass-through because the methodology
does not properly control for maturity.
at rates that are both low and insensitive to market interest rates. Second, while running a deposit franchise incurshigh operating costs (branches, salaries, marketing, technology), these costs do not vary much over time and hence arealso insensitive to interest rates. Thus, even though deposits are short-term, funding via a deposit franchise resemblesfunding with long-term fixed-rate debt."
4
Carrying these insights to banking data, We show that what is measured as low sensitivity of
bank rates to market rates arises for two reasons: (1) intentional rate setting decisions enabled
by market power and (2) the mechanical consequence of comparing the periodic interest earned
or paid on a positive maturity portfolio with changes in a short-term interest rate. A substantial
portion of bank deposits are time deposits, which we show to exhibit low sensitivity largely due to
the mechanical reason. This challenges the notion that imperfect pass-through is a reliable proxy
for market power in bank deposits, instead much more a measure of the relative composition of
time and non-time deposits.
Scale and incremental operating cost differences between banks that operate in different com-
petitive environments are two additional limitations for using impartial rate pass through coef-
ficients as a proxy for a bank’s deposit market power. Concentrated markets tend to be 12 to
14 times smaller in terms of population, aggregate personal income, and aggregate employment
compared to the most competitive markets. We provide suggestive evidence for incremental cost
differences associated with operating in more concentrated markets. Using HHI as a measure of
bank deposit market power, we estimate a 3 basis point lower annual deposit rate, given a one
standard deviation increase in bank market power. This rate advantage is offset by a 23 basis point
increase in annual operating expenses, which clearly pushes against the notion of a positive net
benefit to banks operating in the most concentrated markets.
The paper is structured as follows. We begin with a brief description of the data in Section
2 and of the properties of NIM, interest betas, and the relationship between income betas and
standard measures of duration risk in Section 3. In Section 4, we show that stable NIM and
asset and liability spread beta matching can be a property of a price-taking US Treasury portfolio
that remains exposed to interest rate risk. Section 5 re-examines the robustness of partial rate
adjustment as a measure of bank market power. In Section 6, we discuss the implications of our
results for an empirical perspective on banks. The last section concludes.
5
2 Data
There are several sources of data used in this analysis. We obtain detailed bank-level data from
quarterly regulatory filings of commercial banks collected in multiple forms, most recently forms
FFIEC 031 and FFIEC 041. The quarterly bank data used for this analysis begin in 1985. For this
analysis, we rely only on assets, non-equity liabilities, interest income, and interest expense, from
which we can calculate NIM and the interest income and interest expense returns. To calculate
bank and county level HHI as well as bank and county level deposit amounts, we rely on the
branch office deposit data provide by the FDIC.9
We obtain economic statistics at the county level from the Regional Economic Accounts of the
Bureau of Labor Statistics.10 The annual data series begin in 2000 and end in 2019. Our analysis
uses county level population, employment, and nominal personal income.
We also use monthly yields and returns for US Treasury bonds. We obtain monthly yields on
US Treasuries (UST) for various maturities from the Federal Reserve, monthly returns on a 5-year
constant maturity bond portfolio from CRSP, monthly returns on the value-weighted stock market
and the one-month US Treasury bill, as calculated by Ken French and available on his website. To
calculate interest income and expense sensitivities as well as spread betas we also use the effective
Federal Funds rate (converted to a monthly frequency) published by the Federal Reserve H.15
release.
3 Properties of Interest Income and Expense Betas
Net interest margin (NIM) is a widely referenced operating and interest rate risk metric in bank
financial reports and press releases, the academic banking literature, bank stock analyst reports,
and Federal Reserve reports. NIM is defined as:
9https://www7.fdic.gov/sod/dynaDownload.asp?barItem=610https://apps.bea.gov/regional/downloadzip.cfm
6
NIMt =Interest Incomet− Interest Expenset
Book Assetst−1. (1)
=RInct −RExp
t ,
where RInct is the interest income return and RExp
t is the interest expense return. We examine
several important properties of NIM as a risk metric with a special interest in comparing it to
interest rate risk metrics used in textbook and practitioner bond valuation and in academic asset
pricing research. The goal is to evaluate how much the empirical characteristics of NIM warrant
the interpretation of NIM as a measure of interest rate risk exposure.
3.1 Stable NIM and Matching Income and Expense Betas
In line with views expressed in bank annual reports, Drechsler, Savov, and Schnabl (2021) argue
that stable NIM implies that banks succeed in hedging the interest rate risk embedded in standard
retail banking activities. In particular, they propose that banks rely on the deposit franchise to
offset interest rate risk exposure by intentionally matching the sensitivity of interest income RInct to
changes in the market rate (income beta) to that of interest expenses RExpt (expense beta).11 Indeed,
at the bank level, a regression of the quarterly change of RInct on the quarterly change of the Federal
Funds Rate (FFR) delivers nearly the same OLS coefficient as a regression of the quarterly change
of RExpt on the quarterly change of FFR. Hence, in the cross-section income and expense betas
match neatly.
In this section, we first show that the causality plausibly goes the other way – stable NIM
implies asset and liability beta matching. We provide an empirical example showing that asset and
liability interest spread betas measured against Amazon stock returns instead of the Federal funds
rate also match neatly. Second, we compare income and expense betas to standard interest rate risk
11Spread betas, also known as imperfect pass-through coefficients in the banking literature, are regression coeffi-cients of changes in interest income rate (or expense rate) spreads on changes in a short-term market interest rate.Interest income (expense) rate spreads are measured as a short-term market rate minus the income (expense) rate.Spread betas are related to income (expense) betas as follows: income (expense) beta = 1− spread beta.
7
exposure measures such as DV01 and bond excess return regression betas to assess the robustness
of inferences about interest rate exposure gleaned from these measures.
We begin by assuming that the bank has achieved stable NIM. Perfectly stable NIM means that
NIM is a constant:
NIMt = RInct −RExp
t = RInct−1−RExp
t−1 = NIMt−1 ∀ t ∈ {1, ...,T} . (2)
As a result of constant NIM, any variation in RInct needs to match the variation in RExp
t . Since NIM
is a constant, its covariance with any random variable is 0, COV(NIMt ,X) = 0, for any X . Writing
out the components of NIMt and recognizing that COV(X ,Y +Z) = COV(X ,Y )+COV(X ,Z),
we can write
COV(RInc
t ,X)−COV
(RExp
t ,X)= 0. (3)
We again make use of covariance properties and the fact that Eq. 3 has to hold for ∀ t to write
COV(RInc
t −RInct−1,X
)−COV
(RExp
t −RExpt−1 ,X
)= 0.
Finally, divide by the variance of VAR(X) to derive the coefficients of any regression of changes
in interest income and changes in interest expense on some random variable X :
COV(∆RInc
t ,X)
VAR(X)︸ ︷︷ ︸:=β Inc,X
−COV
(∆RExp
t ,X)
VAR(X)︸ ︷︷ ︸:=β Exp,X
= 0. (4)
Eq. (4) simply says that as long as a bank has achieved stable NIM, the interest income and interest
expense regression coefficients must satisfy
βInc,X = β
Exp,X
regardless of the independent variable X in the regression. In the specific case when X = ∆FFRt ,
8
the coefficients defined by a regression on the federal funds rate (and lags therefore) satisfies the
property that β Inc,FFR = β Exp,FFR.
This highlights that conditional on banks achieving a stable time series of NIM, matching
interest income and interest expense betas at the bank level is a necessary consequence. Figure 2
illustrates this point with asset and liability spread betas measured against Amazon stock returns
instead of the Federal funds rate over the period Q3 1997 to Q4 2020, where Amazon is a publicly
traded firm. The asset and liability Amazon-beta matching is nearly perfect, essentially recreating
the result based on the Federal funds rate. It seems implausible that bank managers intentionally
managed their exposure to Amazon stock, as the causal narrative requires of this evidence.
3.2 Interest Rate Risk Exposure Measures
The sensitivity of NIM and its components, RInct and RExp
t , to changes in short-term market in-
terest rates is sometimes used to assess the interest rate risk exposure of banks (e.g., Hoffmann
et al., 2019; Haddad and Sraer, 2020; Drechsler, Savov, and Schnabl, 2021). To reach conclusions
about the net interest rate exposure of long-short portfolios that have matching interest income and
interest expense betas, these betas must be good measures of interest rate exposure. This section
describes the properties of income betas and compares them to standard interest rate risk exposure
measures.
In this method, the change in NIM, or the change in RInct and RExp
t , is regressed on changes in
the Federal Funds Rate (FFR), resulting in coefficients β FFR. In contrast, standard asset pricing
theory defines interest rate risk, or duration risk, as the change in the value of a portfolio to a change
in interest rates. For example, DV01 defines duration as the change in the asset value for a 1 basis
point change in the interest rate. Another related way to measure interest rate risk is to regress the
periodic excess returns of a portfolio on an interest rate factor, say the 5-year UST market return in
excess of the one-month US T-bill rate. The resulting regression coefficient, β T ERM, captures how
much a portfolio value moves with a 1% movement in the interest rate factor.
9
Income Betas. To see the difference in these two methods for assessing interest rate risk, we
focus first on income betas (or equivalently expense betas). Take a simple example. Assume that
the bank holds a fixed-income portfolio that invests each period the same amount into a bond with
characteristics ms and holds this bond to maturity. The subscript s denotes the period during which
the bond was bought. Bond characteristics can include the maturity and credit risk of the bond.
For simplicity, we assume that each period the bank buys default-free bonds of the same maturity.
Denote with ymss the associated income (coupon) earned each period until its maturity. Abstracting
from default, the income stream for each bond ymss is fixed. Hence, the income rate on the portfolio
and the quarterly change in the income rate are simply:
RInct =
1J
J
∑j=1
ymt− jt− j . (5)
∆RInct+1 =
1J(ymt
t − ymt−Jt−J ). (6)
This simple portfolio example clarifies that the change in the income of the simple fixed income
portfolio only captures the difference between the income of the most recently purchased bond
and the income of the oldest bond in the portfolio, since the coupons associated with all other
bonds purchased in between those dates are fixed and therefore contribute zero to the difference.
Consider attempting to measure interest rate risk using a regression of the change in income to a
change in FFR:
βInc =
COV(∆RInct+1,∆FFRt)
VAR(∆FFRt)(7)
=1J COV(ymt
t ,∆FFRt)
VAR(∆FFRt), (8)
where the second line of Eq. (8) follows from the first because ymt−Jt−J is uncorrelated with ∆FFRt
for J > 1. Adding lags of FFR up to t− J to the regression will measure the covariance of ymt−Jt−J
with ∆FFRt−J . But since the coupons of all other bonds are differenced, the additional lags will
not improve this regression. Additionally, notice that the coefficient is declining in the portfolio
10
strategy maturity, J, as the portfolio weights will be decreasing in maturity for any realistic strategy
that maintains relatively stable exposure.
For example, a portfolio strategy that each month buys a 5-year bond will have 60 holdings and
the difference in interest income returns will be, ∆RInct+1 = 1
60(y60t − y60
t−60). Note that the interest
income from just 2 of 61 positions are affecting this calculation and that the covariance is being
heavily down-weighted by the average position weight, 1/60. Suppose that market yields can be
characterized by the short rate plus a term premium, y60t = y0
t + φ 60t . If φ 60
t is constant through
time, then
COV(∆RInct+1,∆FFRt+1) =
160
COV((y0
t − y0t−60),(FFRt−FFRt−1)
).
In this simplified example, the income beta would just be 1/60 of the contemporaneous covariance
between the change in Federal funds rate and y0t (depending on the definition of y0
t , y0t may simply
be FFRt).
Duration and Term Exposure. Interest rate risk is typically measured via duration (Cochrane,
2009; Berk and DeMarzo, 2019). Duration is the sensitivity of a bond’s j value V jt to a parallel shift
in the current yield curve yt , hence d jt ≡
δV jt
δyt. It is well-known that individual bond sensitivities
tend to be increasing in maturity. The interest rate sensitivity of a bond portfolio is simply the
weighted average duration of the portfolio’s individual bonds d jt , i.e., dp
t = ∑Jj=1 w jd j
t .
Another way to express duration is via excess bond return regressions relative to some bench-
mark bond portfolio, say the constant H-maturity portfolio constructed as in Section 4 that earns
the portfolio return RHt+1 as follows
RHt+1 =
cHt+1 +∆V H
t+1
V Ht
=J
∑j=1
w jt R j
t+1, (9)
where w jt are the portfolio weights of bond j in portfolio H, cH
t+1 is the sum of all coupons on the
portfolio, and ∆V Ht+1 is the change in the value of the bond portfolio H.
11
To see the relationship between this duration measure and an empirical duration measure based
on regressions for a bond k, define first the periodic excess bond k return by subtracting the riskfree
rate from bond’s k return, so
XRkt+1 = Rk
t+1−RFt+1 = exck
t+1 +dkt ∆yt+1 + ek
t+1,
where exckt+1 = ck
t+1−RFt+1 is coupon on bond k in excess of the riskfree rate RF
t+1, dkt ∆yt+1 uses
the fact that the change in the bond value to a shift in the yield curve ∆yt+1 equals dkt , and ek
t+1 was
introduced to allow for return shocks that are uncorrelated with ∆yt+1. We can then calculate the
empirical duration as the regression coefficient of the fitted periodic excess return of bond k on the
fitted constant H-maturity portfolio excess return, which can be expressed as
COV(XRkt+1,XRH
t+1)
VAR(XRHt+1)
=COV(exck
t+1 +dkt ∆yt+1,excH
t+1 +dHt ∆yt+1)
VAR(excHt+1 +dH
t ∆yt+1)
=dkdHVAR(∆yt+1)
(dH)2VAR(∆yt+1)
=dk
dH , (10)
where the second line follows from the first because removing the risk-free rate from the cash
income means removing the only time varying element from cxt+1 from the perspective of t.12
All other cash flows are known ex-ante and uncorrelated with ∆yt+1. Note, that we dropped time
scripts on dxt to denote time series averages. Eq. (10) says that under our assumptions the empirical
duration regression coefficient is simply the ratio of bond k’s duration to the duration of the constant
H-maturity portfolio.13 As a result, the portfolio regression beta of a portfolio of bonds is simply
the weighted average of the relative durations, ∑Jj w j
td j
dH .
Comparing the interest rate risk measures implied by duration or term regressions coefficient
Eq. (10) with the income beta Eq. (8), we can immediately see how fundamentally different these
12For a more detailed derivation, please refer to Appendix A.13With unfitted excess returns in the regression, the regression coefficient would include an additional term related
to the covariance of the ek’s with the eH ’s.
12
two measures are. While the income beta of Eq. (8) measures the covariance of the current market
rate with a single coupon weighted by the longest maturity of the underlying portfolio, the term
regression coefficient implied by Eq. (10), ∑Jj w j
td j
dH , measures the weighted average exposure of
the market returns of all components of the bond portfolio. These two equations also clarify that
income betas will never recover the duration exposure of a portfolio, unless the portfolio consists
only of floating rate bonds in which case the duration is zero. Adding more lags or more data to the
regression behind (8) does not resolve the fundamental issue that changes in fixed interest income
exposures are a different notion of interest rate risk from the standard asset repricing risk notion –
income sensitivity vs. value sensitivity.
In Appendix B and Tables 8 and 9 we present detailed results on how duration and portfolio re-
turn term exposure coefficients differ from income and expense betas for the purpose of measuring
interest rate risk exposure.
4 Stable NIM without a Deposit Franchise or Market Power
The popular narrative emphasizes the essential role of deposits and market power for generating
stable NIM and for eliminating interest rate exposure.14 We first investigate the claim that a deposit
franchise and market power are essential to generate stable NIM. Next, we show that stable NIM
is not informative about a portfolio’s interest rate risk exposure. To empirically evaluate the first
claim, we develop and evaluate a rule-based portfolio strategy that invests only in US Treasury
securities, thereby restricting its access to deposits and any notion of market power. Assessing
the validity of the basic premise will primarily involve a comparison of the time series variation
in actual bank NIM with the time series variation in the UST portfolio NIM. We can then also
14Drechsler, Savov, and Schnabl (2021) compare the smooth NIM of banks with the more volatile NIM of a Treasuryportfolio they constructed. They state "while banks’ interest expense is low and smooth with respect to the Fed fundsrate, the interest expense of the Treasury portfolio closely tracks the Fed funds rate. This is why the NIM crasheswhenever the Fed funds rate rises. Thus, Figure 4 makes clear why the deposit franchise allows banks to engagein maturity transformation without exposing their bottom lines to interest rate risk". This statement implies (a) thatthe deposit franchise is necessary to generate a stable NIM, and (b) that stable NIM means banks are not exposed tointerest rate risk.
13
evaluate to what extent a stable NIM portfolio has near zero interest rate risk.
4.1 A US Treasury Portfolio Strategy for Stable NIM
We develop a range of variants of a long-short UST portfolio strategy that target different levels of
constant NIM over the 1967 to 2020 period. We compare the time series volatility of the resulting
UST portfolio NIM time series with that of banks.
Each month, the strategy selects cash amounts, asset maturity, debt maturity, leverage, and
repurchasing amounts of assets and debt to target a constant level of NIM, NIM∗. We initially
endow the strategy with an asset portfolio comprised of a fraction, ωCasht , in cash (1-month US T-
bill) with the remainder invested equally across a seasoned allocation to UST bonds purchased at
previous dates each with an initial maturity of HA. This portfolio is initially funded with a fraction,
1−D/A, of investor’s equity with the remainder funded with an equally weighted allocation of
UST bonds sold at previous dates with an initial maturity of HD. At the end of each month, the
portfolio accounting and market equity and asset values are updated and then decisions about asset
reinvestment, liability refinancing, and rebalancing of assets and liabilities are made. The portfolio
decision are constrained by the evolution of the balance sheet, a maximum book value leverage
ratio, Dt/At , of 0.9, a maximum rebalancing of 20% of assets and 20% of debt in any period, and
no further access to external equity capital. The updating of the portfolio occurs for the book and
market value balance sheets.
Given the number of choices and the target of constant NIM, there are potentially many solution
methods to this problem. We are simply looking for a method that achieves a relatively stable NIM,
not necessarily the best strategy for this objective. As illustrated in Section 3 and with Eq. 5, the
income or expense on any historical position implies largely predetermined cash flows. That is,
at each point in time, conditional on portfolio holdings being chosen, the next period NIM is
known with certainty since all holdings are fixed income securities. The practical challenge is
having enough slack to make adjustments, given the current market yield curve. For example, if
the entire current yield curve is relatively flat and offering low market interest rates relative to the
14
NIM target, then leverage will need to be low, and leverage will need to have been moving lower
beforehand to satisfy the constraints that limit portfolio rebalancing and restrict access to external
equity. Thus, the algorithm must choose an appropriate forward looking target leverage depending
on the perceived challenge of being able to achieve the constant target NIM in the forward period
where existing assets have yet to mature, but after existing debt matures (i.e. HD to HA). It also has
to take into account what reinvestment asset amounts and refinancing liability amounts generate
the forward looking target leverage and how much rebalancing of assets and liabilities is allowed.
These decisions generate a pro forma NIM for the next period that we can then compare against
the constant target NIM. The strategy then chooses the period t decisions that bring the pro forma
NIM closest to the target. We generate a cross-section of UST portfolios where each is defined by
a set of initial parameter conditions HA,HD,D/A,wCash and a stable NIM∗ target.
4.2 Stable NIM and Spread Beta Matching in UST Portfolios
We explore the properties of a constructed sample of stable NIM portfolios that use the same
set of above mentioned portfolio rules, but differ in their strategy parameters. Specifically, we
consider all permutations of the following strategy parameters: HA ∈ {48, 54, 60, 66}, HD ∈{18,
24, 30}, ωCasht ∈{0.10, 0.15, 0.20, 0.25, 0.30}, D/A ∈{0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80},
and NIM∗ ∈{1.0%, 1.5%, 2.0%, 2.5%, 3.0%}, resulting in 2,100 portfolio strategies.
Table 2 and Figure 3 compare the NIM stability and interest rate sensitivity matching of US
commercial banks to the sample of stable NIM UST portfolios. Panel A of Table 2 summarizes
the mean and time series variation of NIM for the aggregate banking sector and for a similarly
constructed aggregate of the considered UST portfolios. Over the period 1985-2020, bank NIM
has a quarterly standard deviation of 0.090 and the standard deviation of quarterly changes in
bank NIM is 0.031. Over this same period, the quarterly standard deviation of NIM of the UST
portfolios is 0.068 and the standard deviation of quarterly changes in UST portfolio NIM is 0.020.
Interestingly, over the longer sample from 1965-2020 that includes the interest rate spike around
1981, the UST portfolio NIM continues to have a lower standard deviation than bank NIM. The top
15
panel of Figure 3 displays the annualized quarterly NIM for banks and the average UST portfolio,
along with the Federal funds rate. While not the focus of this analysis, it is natural to compare
the mean levels of NIM between the UST portfolios and actual banks. The average annualized
NIM for commercial banks is 3.24% and is 1.57% for UST portfolios. It is helpful to recall that
the interest expense component of deposits is only a portion of the full cost of deposits, since
operating expenses are excluded from NIM; and that the issuance yield on loans is what banks
earn in the absence of losses, but not what they actually earn after losses are realized. It is also
important to note that these UST portfolios are not designed to mimic the maturity composition of
banks, merely to evaluate whether stable NIM can be achieved without deposits.15
A central element in the causal narrative of how banks achieve stable NIM is their asset and
liability interest beta (or spread beta) matching. To evaluate the hypothesis that deposit market
power is essential to the interest beta matching, we explore whether there is any evidence of asset
and liability interest beta matching within the sample of UST portfolios targeting stable NIM. The
bottom panel of Figure 3 shows that there is near perfect interest beta matching within the sample of
UST portfolios. The second and third panels of Table 2 confirms this relation with cross sectional
regressions of income spread betas on expense spread betas (panel B) and income betas on expense
betas (panel C) using the same specifications as in Drechsler, Savov, and Schnabl (2017, 2021).
For comparison, we also include the cross sectional regressions for the banks. The first column
essentially reproduces the results in Drechsler, Savov, and Schnabl (2017, 2021) over a slightly
updated sample period, with nearly identical regression coefficients and R2. The regressions from
the sample of UST portfolios show that the spread beta matching in the sample of UST portfolios
is even stronger than it is in banks, with similar regression coefficients and higher R2. This result
holds over the longer sample period that begins in 1965. The beta matching is consistent with
the analysis in Section 3, showing that conditional on achieving stable NIM approximate beta
15Begenau and Stafford (2020) construct passive capital market portfolios based on the reported maturity and creditrisk holdings of banks and compare the cash flows and returns of these benchmark portfolios to banks. Interpretingtheir results relies on whether bank deposits effectively offset the duration risk of bank assets. Without a near completeoffset of the duration risk of bank assets, Begenau and Stafford find that bank cash flows and returns underperformtheir passive capital market benchmarks.
16
matching is a consequence, not the unique causal mechanism. The finding that both stable NIM
and interest beta matching (and spread beta matching) are achievable in UST portfolios illustrates
that neither deposits nor market power are essential for achieving stable NIM.
4.3 Interest Rate Risk of Stable NIM UST Porfolios
An important recent inference in the banking literature is that banks are able to engage in activities
that create a maturity mismatch between their assets and their liabilities without bearing interest
rate risk (see Drechsler, Savov, and Schnabl, 2017, 2021).16 We now examine the claim that stable
NIM and asset and liability spread beta matching are indicative of near zero interest rate exposure.
We test this hypothesis directly with our sample of stable NIM UST portfolios that exhibit strong
asset and liability interest beta matching.
As in Section 3, we calculate interest rate risk in two standard ways, using a simple fixed
income valuation model and from regressions of market excess returns on a interest rate term
factor, TERM (i.e. the excess return on a constant maturity 5-year UST bond portfolio). At each
point in time, the asset and liability positions in each UST portfolio are known and a simple fixed
income bond valuation model is used to map the fixed coupon, remaining maturity, and current
yield curve into a market value for each position. This same valuation model can be used to
calculate a sensitivity to a constant shock to all current yields, a sensitivity commonly referred
to as duration risk. As we showed in Section 3, the net portfolio duration is the weighted sum
of individual holding durations across both assets and liabilities. Additionally, we can calculate
the market value of the equity of each UST portfolio each quarter, with the quarterly percentage
changes in equity being quarterly returns. The quarterly returns, in excess of the one-month US
T-bill rate are regressed on a TERM factor as an alternative means of measuring interest rate risk
exposure (e.g. Fama and French, 1993). Thus, we can explore the time series and cross sectional
relation between maturity mismatch, model-based estimates of duration risk, and equity excess
return regression estimates of TERM exposure.
16In contrast, many other studies argue that banks bear interest rate risk (e.g., Begenau, Piazzesi, and Schneider,2015; English, Van den Heuvel, and Zakrajšek, 2018; Paul, 2020; Williams, 2020).
17
By construction, the UST portfolios that target a positive stable NIM have a maturity mismatch
between their asset maturity and their liability maturity, given the generally upward sloping US
Treasury yield curve from 1954 to 2020. Figure 4 shows the time series behavior of the aggregate
UST portfolio strategies in terms of leverage and cash share of assets (panel A), asset and liability
maturity per dollar of assets (panel B), and model-based duration risk estimates of assets and liabil-
ities per dollar of assets (panel C). Each quarter, the aggregate UST portfolio has an economically
large maturity mismatch, which coincides with a large duration risk mismatch between assets and
liabilities.
Table 3 summarizes the relation between duration risk and maturity composition of the portfo-
lios with cross sectional regressions. We refer to duration risk as "Delta," measuring the average
value change of a security given a 1% shock to the entire yield curve. Consequently, deltas are
negative, reflecting the negative relation between interest rate shocks and fixed income values. The
dependent variable is the time series average of the quarterly asset or debt delta per dollar assets.
Independent variables are the associated maturity in years for debt, the associated maturity in years
and the cash share for assets, and net delta per dollar of equity regressions include leverage. The
cross sectional relation between duration risk and maturity mismatch are very strong across all
specifications with R2 values ranging from 0.80 to 0.99.
Duration risk is the major risk that fixed income investors worry about. Figure 5 illustrates
why this risk matters. Figure 5 displays the quarterly time series of the Federal funds rate and
the total return index of the aggregate stable NIM UST portfolios and the quarterly drawdowns
(measured as the quarterly total return index measured as a percentage return relative to the pre-
vious maximum price level). In the period leading up to June 1981, US short-term interest rates
increased substantially and the total return index experienced a drop in market value approaching
-40%. The figure also highlights the strong tailwinds that a levered maturity mismatched portfolio
experienced from June 1981 through 2011, as interest rates generally declined, but longer-term
yields were such that this realized trend was unlikely to have been anticipated (Fama, 2006). Ta-
ble 4 reports results from a time series regression of the aggregate equity return, in excess of the
18
one-month US T-bill rate, on the 5-year TERM factor. The coefficient is 1.7 (t-statistic = 56.4) and
the R2 is 0.89, highlighting the strong evidence that this maturity mismatched portfolio has sub-
stantial interest rate risk, despite achieving both stable time series NIM and cross sectional spread
beta matching between assets and liabilities. Table 4 also reports results from a cross sectional
regression of portfolio-level TERM exposures on that portfolio’s average net duration risk per dol-
lar equity. The cross sectional relation between TERM exposures and average net duration risk is
highly statistically reliable with almost all of the variance well explained with an R2 of 0.94.
From a standard valuation perspective, there is little that is surprising in the interest rate ex-
posure analysis, given the transparent nature of the stable NIM UST portfolio strategies. Maturity
mismatch is tightly linked to duration risk, which is tightly linked to equity TERM exposure. The
surprising result is that stable NIM and spread beta matching can coincide with these economically
large interest rate exposures. These results strongly reject the notion that evidence of stable NIM
and spread beta matching can be used to infer that interest rate exposure is near zero.
5 Imperfect Pass-Through as Evidence of Bank Market Power?
Deposit rates appear to imperfectly pass-through market interest rate shocks, even though a large
fraction of deposits are demandable and therefore have zero contractual maturity. This is an im-
portant component of the evidence on bank’s market power in deposits. The idea is that banks
exploit their market power over depositors to set rates optimally instead of setting deposit rates in
lockstep with current market rates. The analyses in this section are organized around two main
observations. First, what is measured as imperfect pass-through or partial adjustment can occur
both because of intentional rate setting and because there is a maturity component to many de-
posits. To see the maturity mechanism easily, recall that there is "imperfect pass-through" in the
income return of a rule-based portfolio strategy that buys-and-holds 5-year US Treasury bonds.
This is clearly not because of intentional rate setting by the portfolio manager, but simply the me-
chanical consequence of the imperfect pass-through measurement methodology when applied to
19
positive maturity portfolios. We explore how important this mechanical maturity component is in
time deposits, which can directly affect inferences for total deposits. Second, beyond the maturity
mechanism, the imperfect pass-through measure remains an incomplete proxy for market power
by implicitly assuming no incremental cost differences and no capital scaling differences across
banks operating in concentrated vs competitive deposit markets. We explore whether these implicit
assumptions are likely to be benign or meaningful for inferences.
5.1 Time Deposits are Different
5.1.1 Market power versus Maturity as Mechanisms for Imperfect Pass-Through
We build on the simple bank portfolio example from Section 3.2, where Eq. (7) defines β Inc in the
context of the income return or equivalently expense rate defined by Eq. (5). Recall that spread
betas are simple transformations of expense or income betas (e.g., β Inc = 1−β spread,Inc). In this
section, we study two mechanisms that affect β Inc: maturity in fixed income portfolio dynamics
and intentional rate setting behavior of banks. We begin with a benchmark case of β Exp in the
context of a price taking portfolio composed of floating rate bonds, where β Exp refers to an expense
rate defined as the interest expense over last period’s assets. For this reason, the expense beta is
affected by the debt-to-asset ratio of banks, DA , through $Expense
$Assets = DA
$Expense$Debt = D
A RL. For simplicity
and without loss of generality, we set DA = 1.
Price taking portfolio with floating rate bond We first develop intuition for the income beta
behavior in the case when funding occurs at short-term capital market rates. That is, we assume the
bank funds itself with floating rate debt, where the rate is RLt = 1+FFRt +φ , i.e. the Fed Funds
rate (reference rate) plus a constant spread. This means
βExp =
COV(∆FFRt ,∆FFRt)
VAR(∆FFRt)= 1. (11)
20
With β Exp = 1, any market rate change is perfectly passed through to a bank’s interest expense
rate.
Market power Suppose banks use their market power to set RLt for ∀ t such that the desired
expense rate sensitivity to the Federal Funds Rate β Exp =COV(∆RL
t ,∆FFRt)VAR(∆FFRt)
is achieved. For instance,
β Exp could be set to a fraction ψ < 1 of the current market rate: RLt = 1+ψFFRt , then:
βExp =
COV(∆(ψFFRt) ,∆FFRt)
VAR(∆FFRt)= ψ. (12)
Hence, β Exp reflects banks ability to pay below market rates. The comparison of the price taking
portfolio with floating rate bonds with the market power cases leads to the standard empirical tests
to determine whether interest expense betas are less than one, or whether spread betas are greater
than zero.
Price taking portfolio with M period bond portfolio held to maturity Finally, consider the
case where the expense rate evolves analogously to Eq. (5) in 3. As a result, the expense beta is
defined analogously to Eq. (8). Only the longest maturity in the portfolio and the contemporaneous
covariance between the federal funds rate and the most recently issued yield factor into the β Exp
measure:
βExp =
1J
COV(yM
t ,∆FFRt)−COV
(yM
t−J,∆FFRt)
VAR(∆FFRt)
=1J
COV(yM
t ,FFRt)−COV
(yM
t ,FFRt−1)
VAR(FFRt−FFRt−1)(13)
Note that Eq. (13) is equivalent to Eq. (8) if past yields are uncorrelated with the current
realization of the FFR. With a specific term structure model in mind, we could explicitly solve Eq.
(13) in terms of the parameters that determine factor dynamics and the term structure. Eq. (13)
clarifies that β Exp/A will be smaller the larger J and the more autocorrelated the federal funds rate
is. Thus, either Eq. (12) or Eq. (13) deliver β Exp < 1. An interest expense beta coefficient less than
21
1 cannot be purely attributed to market power if the deposits include some notion of maturity. The
clearest practical example is time deposits, and therefore also total deposits, which include time
deposits.
5.1.2 Maturity and the Imperfect Pass-through of Time Deposit Rates
Given that time deposits account for a large share of total deposits, and that these accounts by
definition are positive maturity, we investigate the extent to which the maturity mechanism affects
measures of partial adjustment in time deposit rates. Table 5 reports cross sectional regressions of
various deposit partial rate adjustment coefficients on the average market concentration, average
natural log bank size, weighted-average county employment where a bank has deposits (log), the
share of non-time deposits to total deposits, and maturity composition variables. The maturity
composition variables are the average share of deposits within quarterly reported maturity cat-
egories. We separately analyze these relations for transaction deposits, time deposits, and total
deposits. To the extent that transaction deposits have no maturity, then the partial rate adjustment
coefficients for these accounts should properly reflect intentional rate setting. In a univariate re-
gression of transaction deposit spread betas (i.e. a cross section of estimated bank-level partial rate
adjustment coefficients) on HHI, there is a reliably positive relation, although the R2 of 0.02 shows
that the fraction of variance explained is small. A regression that excludes HHI, but includes the
bank control variables has an R2 of 0.11. The specification with HHI and the control variables
finds that HHI continues to be reliably positive.
The second panel of Table 5 shows regressions for time deposits. In addition to the previous set
of bank-level control variables, we also include three variables describing the maturity distribution
of time deposits for each bank, the fraction of time deposits with maturity 3-months to 1-year,
1-year to 3-years, and more than 3-years, with 0 to 3-months being the omitted category. Again,
a univariate regression finds that HHI is reliably positively related to spread beta with essentially
zero R2. The specification with controls, excluding the maturity variables has an R2 of 0.04.
A specification with the maturity variables has an R2 of 0.42, with reliably positive coefficients,
22
suggesting that there is a strong relation between measured partial adjustment coefficients for time
deposits and the maturity of these deposits, as anticipated from equations 8 and 13. Adding all
of the bank controls increases R2 to 0.47. The final specification adds HHI and finds that the
coefficient is indistinguishable from zero. These regressions suggest that what is measured as
partial adjustment for time deposits is mostly describing the maturity composition of these deposits
and reflecting essentially no intentional rate setting behavior by banks. This would be consistent
with time deposits, on average, being competitive, paying equivalent rates to US Treasuries of
equivalent maturity (Fama, 1985).
The third panel of Table 5 shows regressions for bank total deposits. These results blend those
from transaction deposits and time deposits. We include the transaction deposit share of deposits as
an additional independent variable. Consistent with the previous regressions, the relation between
the partial adjustment coefficients of deposits and HHI is statistically reliable, but small with an R2
of 0.006 in a univariate regression. Again, the control variables, especially the maturity variables
explain substantially more of the cross sectional variation.
The regressions in Table 4 highlight that time deposits are different from the non-time deposits
and should be analyzed separately. Figure 6 plots the time series of annualized quarterly trans-
action deposits rates, time deposit rates, and total deposit rates for US commercial banks. All
three rates are grouped into value-weighted portfolios based on their deposit HHI, along with the
Federal funds rate. High HHI is defined as the top tercile of the HHI distribution across banks,
which roughly coincides with the US Department of Justice definition of high market concentra-
tion (HHI above 0.25 on a 0 to 1 scale). Low HHI is defined as the bottom tercile, which roughly
coincides with the FTC’s threshold for medium market concentration (HHI above 0.15 is consid-
ered moderately concentrated).17 There are several things to notice. The imperfect pass-through
of market rates for time deposits can now be understood to reflect their increased maturity as op-
posed to intentional rate setting. Consistent with this interpretation, time deposits, on average, pay
higher interest rates than the Federal funds rate. The annual average rate paid on time deposits
17https://www.justice.gov/atr/herfindahl-hirschman-index
23
is 3.1%, while the Federal funds rate averages 2.4% over this sample period. Only transaction
deposits (non-time deposits) exhibit the tell tale signs of market power – imperfect pass-through
and average rates lower than short-term market rates. Additionally, within the non-time deposits,
the difference in rates between high and low market concentration is inconsequential relative to
the difference between the non-time deposit rate and the Federal funds rate. The average non-time
deposit rate for all banks is 1.02%, which is 1.38% below the average Federal funds rate; while
the average difference in transaction deposit rates for banks operating in concentrated versus non-
concentrated markets is only 0.10%. This will be important for assessing whether operating in
concentrated markets provides banks with a net benefit over banks operating in non-concentrated
markets if doing so leads to positive incremental costs or requires limiting their scale.
5.2 Net Benefits to Operating in Concentrated Deposit Markets
The imperfect pass-through of short-term market rates to bank deposit rates is an imperfect proxy
for market power for reasons beyond the maturity mechanism documented above. A stylized
description of the incremental profits banks earn by operating in concentrated deposit markets
relative to competitive deposit markets would consider an empirical relation like the following:
Incremental Profit =(
RMt −RD,high MP
t −Chigh MPt
)Dhigh MP
t −(RM
t −RD,low MPt −Clow MP
t
)Dlow MP
t ,
where RMt denotes the short term market rate, RD,X MP
t is the deposit rate in markets with "X"
deposit market power, X being either high or low, CX MPt is the operating cost associated with
deposit funding in markets with X market power, DX MPt is the quantity of deposit funding in
markets with X market power. The interest rate spread is only a portion of the net benefit and
therefore only provides an accurate assessment of the benefits of operating in a concentrated market
if incremental costs and incremental scale are inconsequential (for a detailed discussion see (Weyl
and Fabinger, 2013)). These are strong assumptions that we investigate in this section.
24
We characterize the incremental spread benefit to operating in a relatively concentrated market
via regressions of a panel of deposit rates on various measures of market concentration. The market
concentration measures include a bank-level HHI (measured as the weighted average of county
HHI where the bank has deposits), the transaction spread beta, and a residual deposit spread beta
estimated by controlling for the maturity variables (i.e. specification 3 from Panel 3 of Table 5). It
is useful to note that HHI and the transaction spread beta are not highly correlated and that HHI
and the residualized deposit spread beta are essentially uncorrelated with HHI, so these variables
do indeed measure different things. The panel regressions include time fixed effects and standard
errors are calculated with clustering by time and bank.
Table 1: Net benefits
HHI Trans. Resid.Spread Beta Spread Beta
Std 0.119 0.105 0.080Rate Coef x Std (bps) -2.6 -8.9 -7.8Cost Coef x Std (bps) 23.0 8.9 4.9Net Benefit -20.4 0.0 2.9
Table 6 reports results from these regressions and Table 1 provides a simple calculation of
the net-benefit based on the estimated coefficients from Table 6. The first specification simply
includes the time and bank fixed effects to provide a baseline as context for the adjusted R2, which
is 0.85. The second specification adds the bank-level control variables, which are the same ones
used in Table 5, increasing adjusted R2 to 0.93. Each of the coefficients on the three proxies for
bank deposit market power are reliably negative, with minimal improvement in adjusted R2. The
coefficients multiplied by one standard deviation of the associated variable are used to interpret
economic magnitudes and are summarized at the bottom of the panel. A one standard deviation
increase in market power is associated with a 3 to 9 basis point improvement in deposit funding
rates.
We turn now to whether the incremental 3 to 9 basis points improvement in funding rate is
25
large enough to offset the potential cost and scale differences that arise for banks operating in
concentrated markets. We run similar regressions of operating expense rates (non-interest rate
expense scaled by bank assets) on bank characteristics and the market concentration proxies to
measure incremental cost differences. The bank controls continue to include bank size and the
average county size in which the bank operates, but now also include real estate loans and business
loans as a share of deposits. The coefficients on the three proxies for market power tend to be
reliably positive, although the coefficient on the residual deposit spread beta is only marginally
significant. A one standard deviation increase in market power is associated with a 5 to 23 basis
point increase in non-interest expenses. The net benefits (i.e. marginal funding benefit - marginal
operating expense) range from +3 basis points to -20 basis points per year, with the most negative
net benefit associated with the most direct proxy for market power, HHI.
A final analysis investigates the characteristics of counties with high deposit market concen-
tration. We summarize the average county level population, employment, and personal income
conditional on deposit market concentration level in Table 7. There is a strong tendency for highly
concentrated deposit markets to be relatively small places based on either population, employment,
or personal income, consistent with results in Drechsler, Savov, and Schnabl (2017).
Overall, these results cloud the picture of banks benefiting from operating in the most con-
centrated deposit markets. There may be a local market power benefit to transaction deposits that
essentially all banks are able to benefit from based on the partial adjustment analysis of transaction
deposits that shows that even banks operating in the most competitive markets exhibit highly im-
perfect interest rate pass through. However, this inference is constrained by not considering costs.
It is not at all clear that the spread is large enough to cover the costs associated with running the
deposit-taking activity, especially when interest rates are low and the rate paid appears to be con-
strained to be non-negative, resulting in essentially a zero spread (or benefit). In a very low interest
rate environment with positive costs, the deposit-taking activity may well be generating economic
losses.
26
6 Discussion
Interpreting the UST portfolio analysis The key result is that long-short fixed income portfo-
lios can achieve stable NIM, and as a consequence exhibit asset and liability spread beta matching,
without having access to deposits or market power. This requires a dynamic portfolio strategy
that adjusts leverage and strategically rebalances the portfolio based on the relative yields avail-
able in the market via the yield curve and those available inside the portfolio. As a consequence
of constructing a sample of transparent UST portfolio strategies that, on average, have a matu-
rity mismatch between assets and liabilities, the interest rate risk exposures can be measured with
standard methods. While these portfolios share the same properties that have been used in the
literature to conclude that interest rate risk is near zero, they in fact have statistically reliable and
economically large interest rate risk exposure. Thus, our analysis shows that substantial interest
rate risk may reside in portfolios that according to industry-standard performance metrics suggest
no risk exposure at all.18
This main result is simple and intuitive once the distinction between income (expense) betas
and duration risk is recognized. Even though we have shown that interest income or expense
do not reveal the interest rate exposure of banks, our results do not establish that banks do have
interest rate exposure. We only show that the evidence used to conclude that they do not bear
interest rate risk cannot support that conclusion. In order to measure banks’ interest rate risk
exposure the duration risk of deposits must be estimated. There is an earlier literature that estimates
the duration risk of bank deposits and finds that these risks are difficult to empirically measure,
requiring a structural valuation model of bank deposits Hutchison and Pennacchi, 1996; Jarrow
and Van Deventer, 1998; Janosi, Jarrow, and Zullo, 1999; Bolton et al., 2021). An alternative is to
outsource the assessment of banks’ interest rate exposure to the stock market and to estimate these
implied assessments from stock returns. We discuss these inferences below.
There are many important components to the valuation of bank deposits. Two important ones
18During the US interest rate spike in 1981, the average equity value of the UST portfolios loses approximately-40% of its value, while maintaining near constant net interest margin.
27
are operating costs and forecasts of the level of future interest rates. To the extent that time deposits
are approximately competitive (Fama, 1985), the allocation of bank operating costs to transaction
deposits must be high. Additionally, since banks cannot sell short deposits and the stickiness
of deposit customers is likely to be related to the spread between short-term market rates and
transaction deposit rates, and the interest rate appears to be bounded at zero, it is not clear that the
value of deposits is positive when interest rates are low and expected to remain low for a while.19
These are issues to be sorted out with a structural valuation model of bank deposits that allows for
these economic properties as well as the potential for market power. A valuation model of bank
deposits also allows for the estimation of the duration risk of bank deposits, which is a big step
towards a conceptually valid assessment of the net interest rate risk of banks.
Connecting the Results to Banks The focus on US Treasury portfolios can seem detached from
the operations of US commercial banks. It is helpful to recall from Section 5 that in the absence of
market power and operating and regulatory costs, the interest rate paid by banks on time deposits
will resemble US Treasury securities. Additionally, US Treasury securities directly account for
a small portion of the aggregate asset portfolio and underlie the pricing of most other assets that
banks hold.
The analysis shows that a fairly dynamic portfolio strategy is required to achieve stable NIM in
UST securities. It is natural to consider whether banks are likely to be more or less constrained than
the UST portfolio strategies, given their mix of activities. Access to transaction deposits and loans
represent the most unique differences from the UST portfolios. For banks, rebalancing within
existing loans is constrained and short selling of deposits is completely restricted. However, all
else equal, access to more non-redundant activities adds slack to the optimization. Additionally, the
unique properties, in terms of NIM contribution, of loans and transaction deposits add considerable
flexibility. Loans add flexibility because they contribute a credit yield spread without subtracting
losses from NIM, while also contributing zero marking-to-market as market conditions evolve.
This is a significant source of stable interest income, but also clearly an allocation that bears risk.19Bolton et al. (2021) propose a theory where involuntary deposit inflows lower bank valuations.
28
Additionally, loans offer an easy means for "disposing" of excess NIM, as banks can extend credit
at below market rates if stable NIM optimization is the agreed upon objective. Transaction deposits
add a stable interest expense to NIM, but importantly also a relatively low amount of interest
expense, which leads to a higher level of NIM. The interest paid on transaction deposits is likely a
small portion of the full cost of supplying transaction services to customers and therefore offers a
substantial advantage over a strategy that must report its full cost of funding.
This highlights a few important points. First, banks are likely to face a less constrained stable
NIM optimization than the one implemented in UST securities because of the way their unique
activities contribute to the measure. Both loans and deposits contribute stable net income to NIM
and both also exclude substantial associated costs, losses, and risks (i.e. covariance of unexpected
costs and losses with economic states of nature) that are in fact being borne by the equity investors.
The UST portfolio strategies are constrained to trade within a set of assets that do not allow for
similar omissions of costs, losses, and risks. A second related point is that from an economic
perspective, NIM seems to be a highly unusual metric to receive so much practitioner interest. NIM
does appear to be, at least somewhat, optimized to be stable through time. It would be a remarkable
coincidence for an optimized stable NIM strategy to be equivalent to value maximization, given
that the measure omits costs, losses, and systematic risks and essentially makes no use of market
values. Third, to the extent that bank managers view interest income sensitivity to interest rate
shocks as opposed to market value sensitivity to interest rate shocks and make decisions on this
basis there may be some inconsistent pricing of bank and market pricing of related products. This
would lead a bank lender and a non-bank market lender to require different returns on the same
loan, simply because of different definitions of risk.
Comparing to Inferences from the Stock Market It is common to infer risk properties about
firms and sectors from the stock returns of publicly traded firms. Implicit in this analysis is the as-
sumption that stock market valuations, and importantly changes in valuation, accurately reflect the
fundamentals of the firms being analyzed. In general, this is viewed to be a robust empirical design,
29
but in the case of banks there are a few causes for concern about relying too completely on this
methodology. Bank valuation multiples appear to be very strongly related to accounting ROE (net
income divided by Tier 1 capital). Stock market valuations do not distinguish between account-
ing ROE that is generated by attractively selected risks (positive risk-adjusted performance) and
simply increased risk premia (zero or even negative risk-adjusted performance). In other words,
the stock market will pay more for dollar of earnings from a highly levered underperforming bank
than for a low levered outperforming bank. Additionally, stock return implied risk measures for
banks predict realized risks substantially worse than simple rankings based on risk-weighted assets
to tier 1 capital (Begenau and Stafford, 2020). The risks implied from bank stock returns suggest
that banks have little interest rate risk, have little credit risk, and strongly resemble the risks of
ordinary non-bank corporations. At the same time, the level and time series patterns of bank cash
flows are well described by portfolios constructed to mimic the reported duration and credit risk of
bank activities (Begenau and Stafford, 2020).
7 Conclusion
The analysis in this paper demonstrates that the evidence used to reach conclusions about bank
interest rate risk exposure being near zero does not support that conclusion. We show that in a
sample of transparent US Treasury portfolio strategies, sharing the empirical properties that have
been used in the literature to conclude that interest rate risk is near zero, that these portfolios have
statistically reliable and economically large interest rate risk exposure. For example, during the
US interest rate spike in 1981, the average equity value of the UST portfolios loses nearly -40%
of its value, while maintaining near constant net interest margin. This evidence does not establish
that banks do bear interest rate risk, which requires properly assessing the duration risk offset that
transaction deposits may provide (see Hutchison and Pennacchi, 1996; Jarrow and Van Deventer,
1998; Janosi, Jarrow, and Zullo, 1999), but highlights that substantial interest rate risk can reside
in portfolios that according to industry-standard performance metrics suggest no risk at all.
30
The analysis also suggest that the cross-section of market power translates into very small con-
sequences for bank funding rates, which are essentially offset by increased non-interest expenses.
To the extent that there is bank deposit market power, all banks appear to have it, with the cross
section of bank deposit market power appearing to be relatively inconsequential. This has impli-
cations for research relying on a meaningful cross section of bank deposit market power in their
empirical design.
31
References
Ausubel, Lawrence M. 1992. “Rigidity and asymmetric adjustment of bank interest rates.” Kellogg
Working Paper .
Begenau, Juliane, Monika Piazzesi, and Martin Schneider. 2015. “Banks’ risk exposures.” Tech.
rep., National Bureau of Economic Research.
Begenau, Juliane and Erik Stafford. 2020. “Do Banks have an Edge?” SSRN 3095550 .
Berger, Allen N and Timothy H Hannan. 1989. “The price-concentration relationship in banking.”
The Review of Economics and Statistics :291–299.
Berk, Jonathan and Peter DeMarzo. 2019. Corporate Finance. Pearson Higher Ed.
Bolton, Patrick, Ye Li, Neng Wang, and Jinqiang Yang. 2021. “Dynamic banking and the value of
deposits.” Tech. rep., National Bureau of Economic Research.
Cochrane, John H. 2009. Asset pricing: Revised edition. Princeton university press.
Diebold, Francis X and Steven A Sharpe. 1990. “Post-deregulation bank-deposit-rate pricing: The
multivariate dynamics.” Journal of Business & Economic Statistics 8 (3):281–291.
Drechsler, Itamar, Alexi Savov, and Philipp Schnabl. 2017. “The deposits channel of monetary
policy.” The Quarterly Journal of Economics 132 (4):1819–1876.
———. 2021. “Banking on deposits: Maturity transformation without interest rate risk.” The
Journal of Finance 76 (3):1091–1143.
Driscoll, John C and Ruth Judson. 2013. “Sticky deposit rates.” Available at SSRN 2241531 .
English, William B, Skander J Van den Heuvel, and Egon Zakrajšek. 2018. “Interest rate risk and
bank equity valuations.” Journal of Monetary Economics 98:80–97.
32
Fama, Eugene F. 1985. “What’s different about banks?” Journal of monetary economics 15 (1):29–
39.
———. 2006. “The behavior of interest rates.” The Review of Financial Studies 19 (2):359–379.
Fama, Eugene F and Kenneth R French. 1989. “Business conditions and expected returns on stocks
and bonds.” Journal of financial economics 25 (1):23–49.
———. 1993. “Common risk factors in the returns on stocks and bonds.” Journal of Financial
Economics 33:3–56.
FDIC. 1997. History of the Eighties–lessons for the Future: An examination of the banking crises
of the 1980s and early 1990s, vol. 1. Federal Deposit Insurance Corporation.
Gomez, Matthieu, Augustin Landier, David Sraer, and David Thesmar. 2021. “Banks’ exposure
to interest rate risk and the transmission of monetary policy.” Journal of Monetary Economics
117:543–570.
Granja, João, Christian Leuz, and Raghuram Rajan. 2018. “Going the extra mile: Distant lending
and credit cycles.” Tech. rep., National Bureau of Economic Research.
Haddad, Valentin and David Sraer. 2020. “The banking view of bond risk premia.” The Journal of
Finance 75 (5):2465–2502.
Hannan, Timothy H and Allen N Berger. 1997. “The rigidity of prices: Evidence from the banking
industry.” J. Reprints Antitrust L. & Econ. 27:245.
Hannan, Timothy H and J Nellie Liang. 1993. “Inferring market power from time-series data: The
case of the banking firm.” International Journal of Industrial Organization 11 (2):205–218.
Hoffmann, Peter, Sam Langfield, Federico Pierobon, and Guillaume Vuillemey. 2019. “Who bears
interest rate risk?” The Review of Financial Studies 32 (8):2921–2954.
33
Hutchison, David E and George G Pennacchi. 1996. “Measuring rents and interest rate risk in
imperfect financial markets: The case of retail bank deposits.” Journal of Financial and Quan-
titative Analysis :399–417.
Janosi, Tibor, Robert A Jarrow, and Ferdinando Zullo. 1999. “An empirical analysis of the Jarrow-
van Deventer model for valuing non-maturity demand deposits.” The Journal of Derivatives
7 (1):8–31.
Jarrow, Robert A and Donald R Van Deventer. 1998. “The arbitrage-free valuation and hedging of
demand deposits and credit card loans.” Journal of Banking & Finance 22 (3):249–272.
Jiang, Erica Xuewei and Anthony Lee Zhang. 2021. “The Bank Churn Channel.” Tech. rep.,
Chicago Booth.
Neumark, David and Steven A Sharpe. 1992. “Market structure and the nature of price rigid-
ity: evidence from the market for consumer deposits.” The Quarterly Journal of Economics
107 (2):657–680.
Paul, Pascal. 2020. “Banks, Maturity Transformation, and Monetary Policy.” Federal Reserve
Bank of San Francisco.
Reserve, Federal. 2013. “Savings and Loan Crisis.” https://www.federalreservehistory.org/essays/
savings-and-loan-crisis.
Wang, Olivier. 2018. “Banks, low interest rates, and monetary policy transmission.” NYU Stern
School of Business .
Wang, Yifei, Toni M Whited, Yufeng Wu, and Kairong Xiao. Forthcoming. “Bank market power
and monetary policy transmission: Evidence from a structural estimation.” Journal of Finance .
Weyl, E. Glen and Michal Fabinger. 2013. “Pass-Through as an Economic Tool: Principles of
Incidence under Imperfect Competition.” Journal of Political Economics 121:528–583.
34
Williams, Emily. 2020. “Heterogeneity in Net-Interest Income Exposure to Interest Rate Risk and
Non-Interest Expense Adjustment.” Available at SSRN 3559364 .
35
Table 2: Comparing Interest Rate Sensitivity Matching of Banks and UST Portfolios
Banks UST UST1985-2020 1985-2020 1965-2020
NIM StabilityMean NIM 0.810 0.393 0.424
Std NIM 0.090 0.068 0.072
Mean dNIM -0.001 -0.001 -0.001Std dNIM 0.031 0.020 0.027
N 144 144 224
Spread betasSB Inci = b0 +b1×SB Expi + ei
Intercept 0.094 0.059 -0.032t-stat (10.62) (10.11) (-5.63)
Slope 0.828 0.834 1.014t-stat (59.72) (75.09) (104.86)
R2 0.30 0.73 0.84N 8,484 2,100 2,100
Income betasB Inci = b0 +b1×B Expi + ei
Intercept 0.078 0.107 0.018t-stat (14.96) (19.80) (4.40)
Slope 0.828 0.834 1.014t-stat (59.72) (75.09) (104.86)
R2 0.30 0.73 0.84N 8,484 2,100 2,100
Notes: This table reports summary statistics and regression coefficients for US commercial banks and US Treasury(UST) portfolio strategies that target stable NIM. The first column uses data from an aggregate sample of US com-mercial banks from 1985 Q1 to 2020 Q1. An aggregate sample of stable UST portfolios from 1985 Q1 to 2020 Q1is presented in the second column and from 1965 Q1 to 2020 Q1 in the third column. The top panel presents the an-nualized percentage mean and standard deviation of NIM and the quarterly change in NIM for all three samples. Themiddle panel presents the cross-sectional regression results of asset income spread betas regressed on liability expensespread betas. Spread betas are calculated as bank or UST portfolio-level OLS coefficients from regressions of changesin the spread between the Federal funds rate and bank or UST portfolio interest rates on changes in the Federal fundsrate with four lags. The bottom panel displays the cross-sectional regression results of asset income betas regressed onliability expense betas. Income (expense) betas are calculated as bank or UST portfolio-level OLS coefficients fromregressions of changes in bank or portfolio income (expense) rates on changes in the Federal funds rate with four lags.Bank data comes from commercial bank call reports (FFIEC 031 and 041).
36
Table 3: Duration Risk Explained by Maturity Mismatch
Intercept Debt Mat. Asset Mat. Cash Shr Leverage R2 / N
Debt Delta / A 0.00 -0.01 0.99(9.42) (-119.62) 222
Asset Delta / A -0.02 0.00 0.16(-9.23) (6.65) 222
Asset Delta / A -0.05 0.00 0.19 0.80(-32.40) (19.23) (26.39) 222
Net Delta / A -0.04 0.01 -0.01 0.14 0.96(-19.46) (31.98) (-25.01) (13.72) 222
Net Delta / E 0.06 0.04 -0.01 -0.10 -0.14 0.88(4.63) (12.57) (-10.58) (-1.45) (-26.16) 222
Notes: This table summarizes the relation between duration risk and maturity composition of the stable NIM USTportfolio strategies using regression results. The dependent variable is duration risk "Delta" calculated as the averagevalue change of a security given a 1% shock to the entire yield curve. Deltas are calculated for a time series of debtand asset values of each portfolio per dollar of assets. Net Delta are expressed per dollar of assets and equity value,respectively. The independent variables are the associated maturity in years for debt and the associated maturity inyears and the cash share for assets to which the net delta regressions add leverage.
37
Table 4: 5yr TERM Exposure of UST Stable NIM Strategies (Monthly)
Intercept MKT-RF 5yr TERM R2 / N
Total Return Index 0.00 -0.03 0.00(3.77) (-1.05) 399
Total Return Index 0.00 1.74 0.89(0.29) (56.02) 399
Total Return Index -0.00 0.02 1.75 0.89(-0.17) (2.71) (56.44) 399
Cross Section of 5yr TERM Exposure Explained by Net Delta / MV Equity
Intercept Net Delta R2 / N
5yr TERM Exposure -0.31 -30.91 0.94(25.95) (185.88) 2,100
Notes: This table summarizes the interest rate exposures of stable NIM UST portfolio strategies. The top panel presentsthe results from a monthly time series regression of the aggregate stable NIM UST portfolio equity return, in excess ofthe one-month US T-bill rate on the market excess return of a 5-year constant maturity portfolio, 5-year TERM factor,controlling for the market excess return provided by Kenneth French’s website. The bottom panel shows the resultof a cross-sectional regression of portfolio-level TERM exposures on the portfolio-level net delta. The portfolio-levelTERM exposure is calculated as a time series regression of the portfolio-level equity excess return on the TERMfactor. The portfolio-level net delta is calculated as the average value change of the portfolio in response to a 1% shiftof the entire yield curve per portfolio-level market equity value.
38
Table 5: Cross-Sectional Regressions explaining Imperfect Deposit Rate Pass-Through
Transaction Deposits Constant HHI log Assets log Emp. 3m-1y 1y-3y 3y+ TrShr avgR2
1 0.763 0.129 0.018(211.04) (8.77) 4055
2 1.166 -0.026 -0.003 -0.043 0.111(69.00) (-16.85) (-2.79) (-3.14) 4055
3 1.125 0.078 -0.027 0.000 -0.04 0.115(58.68) (4.43) (-17.42) (0.30) (-2.93) 4055
Time Deposits Constant HHI log Assets log Emp. 3m-1y 1y-3y 3y+ TrShr avgR2
1 0.476 0.048 0.002(129.75) (3.24) 4056
2 0.674 -0.005 -0.01 -0.03 0.041(38.15) (-2.86) (-9.00) (-2.12) 4056
3 0.289 0.053 0.652 0.582 0.42(20.07) (2.18) (30.80) (16.03) 4056
4 0.547 -0.015 -0.006 -0.035 0.629 0.572 0.069 0.471(24.43) (-12.28) (-7.18) (-1.44) (30.53) (16.36) (6.43) 4056
5 0.55 -0.006 -0.015 -0.006 -0.035 0.627 0.573 0.069 0.471(22.96) (-0.43) (-11.99) (-6.06) (-1.45) (29.98) (16.36) (6.38) 4056
Deposits Constant HHI log Assets log Empl. 3m-1y 1y-3y 3y+ TrShr avgR2
1 0.615 0.06 0.006(203.48) (4.88) 4056
2 0.763 -0.021 -0.003 0.274 0.197(57.25) (-17.58) (-3.92) (25.59) 4056
3 0.71 -0.548 0.206 0.221 0.167(169.65) (-26.63) (5.00) (3.14) 4056
4 0.615 -0.024 -0.002 0.007 0.486 0.783 0.455 0.308(16.64) (-21.31) (-2.73) (0.13) (10.34) (10.51) (12.38) 4056
5 0.576 0.058 -0.025 0.000 0.012 0.520 0.756 0.466 0.312(15.21) (4.50) (-21.83) (0.42) (0.23) (10.95) (10.13) (12.66) 4056
Notes: This table presents cross-sectional regressions explaining deposit spread betas, a measure of the imperfect pass-through of market rates ondeposit rates. The deposit spread beta is calculated as the OLS regression coefficient of a bank’s quarterly change in its deposit rate on the quarterlychange in the Federal funds rate. The dependent variable in the top panel is the bank-level transaction deposit spread beta, in the middle panel thebank-level time deposit spread beta, and in the bottom panel the total deposit spread beta. The independent variables are HHI as a measure of abank’s market concentration, the average log size of bank assets, and the average log number of employment (in 1000s) of the counties the bank hasdeposits, weighted by the amount the bank’s deposits in each county. The time deposit and total deposit spread beta regressions include the maturitydistribution of time deposits. The time deposit maturity information is the share of time deposits maturing in less than 3 months (omitted), between3 months and 1 year, between 1 year and 3 years, and more than 3 years. The deposit spread beta regression includes the transaction deposit share.Bank deposit rates and maturity data are from commercial bank reports (FFIEC 031 and 041 filings) from 2000 Q1 to 2019 Q1. HHI and deposits atthe bank-county level are calculated based on branch-level data provided by the FDIC "Branch Office Deposits". County level employment statisticsare from the Bureau of Labor Statistics. T-stats are in parentheses.
39
Table 6: Benefits and Costs of Market Power
Deposit RateInt HHI Trs. Spread β Res. Spread β log Asset log Emp. 3m-1y 1y-3y 3y+ TrD/D Adj R2
0.834 0.845(6968.51) 72,594
1.054 0.040 -0.100 1.388 2.127 2.199 -1.199 0.928(6.27) (4.15) (-1.72) (5.26) (6.15) (6.50) (-4.48) 72,594
1.358 -0.220 0.044 -0.216 1.364 2.064 2.218 -1.229 0.928(7.04) (-5.95) (4.43) (-3.39) (5.20) (5.97) (6.66) (-4.59) 72,594
2.174 -0.856 0.018 -0.120 1.340 1.909 2.201 -1.319 0.933(5.43) (-3.70) (3.31) (-2.12) (5.09) (5.07) (6.63) (-4.43) 72,594
1.167 -0.974 0.017 -0.120 1.658 2.284 2.469 -0.957 0.931(6.10) (-3.41) (3.49) (-2.07) (6.57) (7.15) (8.57) (-4.71) 72,594
Non-interest expense / DepositsInt HHI Trs. Spread β Res. Spread β log Asset log Emp. RE L/D C&I L/D TrD/D Adj R2
3.504 0.005(7199.42) 71,958
1.379 -0.136 1.085 0.638 1.463 1.058 0.032(2.97) (-3.89) (5.33) (2.57) (3.64) (3.08) 71,958
-1.060 1.931 -0.173 2.092 0.691 1.451 1.118 0.045(-1.81) (4.23) (-6.03) (9.22) (2.88) (3.68) (3.47) 71,958
0.404 0.850 -0.118 1.069 0.697 1.711 1.123 0.035(0.75) (3.64) (-3.36) (5.25) (2.86) (4.33) (3.21) 71,958
1.223 0.620 -0.124 1.080 0.667 1.617 1.030 0.033(2.41) (1.42) (-4.05) (5.36) (2.60) (3.73) (3.11) 71,958
Notes: This table presents results from annual panel regressions explaining the annualized bank deposit rates (top panel) and annualized bankoperating expenses (bottom panel). The independent variables include three measures of market power: HHI, the transaction deposit spread beta,and on the time deposit maturity distribution residualized total deposit spread beta. In addition, they include the average log size of bank assetsand the average log number of employment (in 1000s) of the counties the bank has deposits, weighted by the amount the bank’s deposits in eachcounty. The deposit rate regression in the top panel include the transaction deposit share and the maturity distribution of time deposits measuredas the shares maturing in less than 3 months (omitted), between 3 months and 1 year, between 1 year and 3 years, and more than 3 years. Thedependent variable in the bottom panel is the annualized non interest expenses as a fraction of deposits. The additional independent variables arethe shares of real estate loans, commercial and industrial loans, and transaction deposits in deposits. The annual sample covers the years from 2000to 2019. Bank deposit rates and maturity data are from commercial bank reports (FFIEC 031 and 041 filings). HHI and county level bank depositsare calculated based on branch-level data provided by the FDIC "Branch Office Deposits". Annual county level employment statistics are from theBureau of Labor Statistics. T-stats are in parentheses. T-stats are in parentheses.
40
Table 7: Characteristics of Deposit Market Concentration
2000 2009 2019 Average Normalized(2000 - 2019) Average
Bank Deposits ($MM) by County Deposit Market Concentration
Bottom Third 2,921 4,103 6,432 4,525 4.8Middle Third 621 2,030 3,515 2,181 2.3Highest Third 242 871 1,723 935 1.0
Population (MM) by County Deposit Market Concentration
Bottom Third 214 221 242 225 11.8Middle Third 50 63 63 59 3.1Highest Third 15 20 20 19 1.0
Employment (MM) by County Deposit Market Concentration
Bottom Third 127 124 150 131 12.8Middle Third 28 38 41 36 3.5Highest Third 8 10 11 10 1.0
Personal Income (MM) by County Deposit Market Concentration
Bottom Third 6,850 8,811 13,863 9,682 14.0Middle Third 1,328 2,407 3,551 2,404 3.5Highest Third 359 672 895 693 1.0
Avg Spread Beta (x100) by County Deposit Market Concentration
Bottom Third 75 75 75 75 1.0Middle Third 75 74 75 75 1.0Highest Third 75 75 75 75 1.0
Avg HHI (0-100) by County Deposit Market Concentration
Bottom Third 16 15 16 15 0.3Middle Third 29 27 28 27 0.5Highest Third 63 59 60 59 1.0
Notes: This table present aggregate statistics based on county deposit market concentration as measured by tercilesof the county level HHI distribution. The annual sample covers the years from 2000 to 2019. Bank deposit rates andmaturity data are from commercial bank reports (FFIEC 031 and 041 filings). HHI and county level bank deposits arecalculated based on branch-level data provided by the FDIC "Branch Office Deposits". Annual county level economicstatistics are from the Bureau of Labor Statistics.
41
Figure 1: Summary of the Literature
1996 2001 2006 2011 2016 20210
2
4
6
8
10Partial Adjustment of Deposit Rates
Deposit Rate
Fed Funds Rate
1996 2001 2006 2011 2016 20210
2
4
6
8
10Net Interest Margin is Stable
Net Interest Margin (NIM)
Fed Funds Rate
0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9
Liability Spread Beta (Proxy for Market Power in Deposits)
0.45
0.5
0.55
0.6
0.65
0.7
0.75
Asse
t S
pre
ad
Be
ta
Asset and Liability Spread Beta Matching
Notes: This figure displays three empirical properties of US commercial bank interest rates. The top panel plots theaggregate interest rate paid on deposits, calculated as the ratio of sums across banks of interest expense on depositsand deposits. The interest rate is annualized by multiplying the quarterly rate by 4. The Federal funds rate isdisplayed for comparison. The middle panel displays a scatter plot of asset spread betas against liability spread betas.Spread betas are calculated via regressions of changes in the Federal funds rate (FFR) minus the interest income(expense) rate on changes in the FFR and four lags of the changes in FFR. We form 50 equally sized bins based on thedistribution of liability spread betas and calculate the average spread beta within each bin. The bottom panel displaysthe annualized aggregate net interest margin (NIM) and the Federal funds rate. Aggregate quarterly NIM is calculatedas the ratio of the sum of interest income minus interest expense divided by the sum of book value of assets.
42
Figure 2: Matching Amazon Stock Return Betas
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5
Liability-AMZN Beta 10-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
Asse
t-A
MZ
N B
eta
10-3
Notes: This figure presents a scatter plot of asset betas against liability betas calculated via regressions of a bank’squarterly income (expense) rate on changes in the quarterly stock return of Amazon up to four lags. We form 50equally sized bins based on the distribution of liability Amazon betas and calculate the average asset beta within eachbin. Amazon stock return data is from CRSP. The sample is from 1997 Q1 to 2019 Q4.
43
Figure 3: Stable NIM UST Portfolios and Matching Betas
1971 1981 1991 2001 2011 20210
2
4
6
8
10
12
14
16
18
20Annualized NIM
UST Portfolio Strategy
Banks
Federal Funds Rate
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75
Liability Spread Beta
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
Asse
t S
pre
ad
Be
ta
Asset and Liability Spread Beta Matching
Notes: This figure displays two properties of US Treasury (UST) portfolios that each target stable net interestmargins. The top panel plots the annualized aggregate net interest margin (NIM) of a cross-section of stable NIMUST portfolio strategies and the Federal funds rate. Aggregate quarterly NIM is calculated as the ratio of the sum ofinterest income minus interest expense divided by the sum of book value of assets. The Federal funds rate is displayedfor comparison. The bottom panel displays a scatter plot of associated asset spread betas against liability spreadbetas. Spread betas are calculated via regressions of changes in the Federal funds rate (FFR) minus the UST portfoliointerest income (expense) rate on changes in the FFR and four lags of the changes in FFR. We form 20 equally sizedbins based on the distribution of liability spread betas and calculate the average spread beta within each bin.
44
Figure 4: Average Properties of Stable NIM UST Portfolio Strategies
1971 1981 1991 2001 2011 20210
0.2
0.4
0.6
0.8
1
Sh
are
of B
ook A
sset
UST Portfolio Strategy Balance Sheet Properties
Average Leverage
Average Cash Share
1971 1981 1991 2001 2011 20210
1
2
3
4
5
6
Matu
ity in
Years
UST Portfolio Strategy Maturity Properties
Asset Maturity per $Assets
Liability Maturity per $Assets
1971 1981 1991 2001 2011 2021-0.04
-0.03
-0.02
-0.01
0
Se
nsitiv
ity t
o 1
% C
han
ge in
Sh
ort
-te
rm I
nte
rest
Ra
te
UST Portfolio Strategy Duration Risk
Notes: This figure displays average properties of US Treasury (UST) portfolios that all target stable net interestmargins. The top panel plots the time series of average portfolio leverage and cash share. Average leverage iscalculated as the average ratio of each UST portfolio’s book value of debt divided by the book value of assets.Average cash share is calculated as the average ratio of each UST portfolio’s cash holding divided by the book valueof assets. The middle panel displays the average maturity in years of assets and liabilities of the stable NIM USTportfolios. The bottom displays the average duration risk of the assets and the liabilities of the stable NIM portfoliostrategies. Duration risk is calculated as the average change in the value of assets and liabilities to a 1% change in theshort-term market interest rate.
45
Figure 5: Portfolio Risk
1971 1981 1991 2001 2011 2021-40
-30
-20
-10
0
10
20
Equity Drawdown
Federal Funds Rate
1971 1981 1991 2001 2011 20210
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0
2
4
6
8
10
12
14
16
18
Fe
de
ral F
und
s R
ate
Log Total Return Index
Index Trend
Federal Funds Rate
Notes: This figure visualizes the risk embedded in the stable NIM UST portfolios. The top panel presents the equitydrawdown calculated as the percentage between a market value peak and the subsequent trough of the aggregatestable NIM UST portfolios. The aggregate stable NIM UST portfolio is simply the sum of all individual portfolios.The Federal funds rate is plotted in green as an annualized percentage rate. The bottom panel presents the log totalreturn index of the aggregate stable NIM UST portfolio along with its trend (left axis). The federal funds rate isplotted in green as an annualized percentage rate (right axis).
46
Figure 6: Imperfect Pass-Through in Deposits and Market Power
1996 2001 2006 2011 2016 20210
2
4
6
8Transaction Deposits
Low Mkt Concentration
High Mkt Concentration
Fed Funds Rate
1996 2001 2006 2011 2016 20210
2
4
6
8Time Deposits
1996 2001 2006 2011 2016 20210
2
4
6
8Deposits
Notes: The figure plots the time series of annualized quarterly transaction deposit rates (top panel), time deposit rates(middle panel), and total deposits (bottom panel) for US commercial banks grouped into portfolios based on theirdeposit market power as measured by the top (high) and bottom (low) tercile Herfindahl-Hirschman Index (HHI)together with the Federal funds rate (green line). Bank interest rate data is from commercial bank reports (FFIEC031 and 041 filings) from 1994 Q1 to 2020 Q1. HHI is calculated based on branch-level data provided by the FDIC"Branch Office Deposits".
47
Appendix A Derivation of empirical duration
In an asset pricing context, the interest rate risk is typically defined as a portfolio value sensitivity
to changes in interest rates. With a simple bond valuation model that maps coupons, remaining
maturity, and the current term structure of market yields into values, duration-style measures can
be calculated for individual holdings and aggregated into a portfolio duration estimate. It is also
common to estimate interest rate risk exposure via regressions of portfolio excess returns on the
excess returns on a constant maturity bond portfolio.
In this section, we show how analytical duration measures are related to regression based dura-
tion measures, and we will contrast these two with the income beta measure defined in the earlier
section. Consider the same portfolio strategy defined above, holding equal amounts of J-maturity
bonds entered into evenly over the past J-months. Each of these holdings has a portfolio weight,
w jt−1, and a market value, V j
t , such that the portfolio value is, V pt = ∑
Jj=1 w j
t−1V jt . We define dura-
tion as the sensitivity of V jt to a parallel shift in the current yield curve, d j
t ≡δV j
tδyt
. It is well-known
that individual bond sensitivities tend to be increasing in maturity. The portfolio value sensitivity
to a parallel shift in the yield curve can be calculated as the weighted sum of the individual d jt , i.e.,
dpt = ∑
Jj=1 w jd j
t .
To see the relationship between this duration measure and an empirical duration measure based
on regressions, define the periodic return on the portfolio,
Rpt+1 =
cpt+1 +∆V p
t+1
V pt
=J
∑j=1
w jt R j
t+1, (14)
where cpt+1 is the sum of coupons collected from all J bonds in the portfolio over the period, and
R jt+1 denotes the return of bond holding j. The periodic portfolio return is related to a change in
the yield curve only through changes in market values,δRp
t+1δyt+1
= 1V p
t
δV pt+1
δyt+1≡ Dp
t , since the coupons
are fixed. Dpt denotes the sensitivity of the portfolio return with a change in the yield curve. It is
useful to note that the portfolio value sensitivity to interest rate changes makes use of all of the
48
holdings.
The empirical duration measure is the coefficient from a regression of portfolio excess returns
on the periodic return on a constant H-maturity portfolio, RHt+1 =
cHt+1+∆V H
t+1V H
t. If H = 5yrs, then this
is the periodic return on a 5yr bond. Before we derive the relation between the empirical duration
measure and dpt , note that we can write the periodic return on any bond x as
Rxt+1 =
1V x
t
(cx
t+1 +∆V Ht+1),
=1
V xt
(cx
t+1 +dxt ∆yt+1
),
=1
V xt
(cx
t+1 + dxt ∆yt+1 + ex
t+1), (15)
where the second equality used the definition for duration dxt and the third equality just follows
from allowing for the possibility of shocks ext+1 to the return that are uncorrelated with shocks to
yt+1. In what follows, we will use Eq. (15) to define the empirical duration. To this end, we abuse
notation and redefine zx = zxV xt . Then, we calculate an excess return on the bond x by subtracting
the riskfree rate from the bond return, so
XRxt+1 = Rx
t+1−RFt+1 = excx
t+1 +dxt ∆yt+1 + ex
t+1,
where excxt+1 = cx
t+1−RFt+1. To abstract from potential measurement issues or other forces than
duration risk that affect XRxt+1, we study the regression coefficient of the fitted periodic excess
return of bond j on the fitted constant H-maturity portfolio excess return. We can express this
regression coefficient as
COV(XR jt+1,XRH
t+1)
VAR(XRHt+1)
=COV(exc j
t+1 +d jt ∆yt+1,excH
t+1 +dHt ∆yt+1)
VAR(excHt+1 +dH
t ∆yt+1)
=d jdHVAR(∆yt+1)
(dH)2VAR(∆yt+1)
=d j
dH , (16)
49
where the second line follows from the first because removing the risk-free rate from the cash
income means removing the only time varying element from cxt+1 from the perspective of t. All
other cash flows are known ex-ante and uncorrelated with ∆yt+1. Note, that we dropped time
scripts on dxt to denote time series averages. Eq. (16) says that under our assumptions the empirical
duration regression coefficient is simply the ratio of bond j’s duration to the duration of the constant
H-maturity portfolio.20 As a result, the portfolio regression beta is simply the weighted average of
the relative durations, ∑Jj w j
td j
dH .
Comparing the interest rate risk measures implied by duration or term regressions coefficient
(Eq. (16)) with the income beta (Eq. (8)), we can immediately see how fundamentally different
these two measures are. While the income beta of Eq. (8) measures the covariance of the current
market rate with a single coupon weighted by the longest maturity of the underlying portfolio, the
term regression coefficient implied by Eq. (16), ∑Jj w j
td j
dH , measures the weighted average exposure
of the market returns of all components of the bond portfolio. These two equations also clarify that
income betas will never recover the duration exposure of a portfolio, unless the portfolio consists
only of floating rate bonds in which case the duration is zero. Adding more lags or more data to the
regression behind (8) does not resolve the fundamental issue that changes in fixed interest income
exposures are a different notion of interest rate risk from the standard asset repricing risk notion –
income sensitivity vs. value sensitivity.
Appendix B Properties of Interest Rate Risk Measure
We now explore the properties of interest rate risk measures in the context of UST bond portfolios
empirically. To design the UST bond portfolios in accordance with the available maturity informa-
tion on bank deposits and asset portfolios, we modify our UST bond portfolios as follows. For a
portfolio that buys each period bonds of maturity H, rather than holding the bond to maturity we
sell any bonds in the portfolio that reached h < H. The income return includes the sales proceeds
20With unfitted excess returns in the regression, the regression coefficient would include an additional term relatedto the covariance of the e j’s with the eH ’s.
50
from bonds with maturity h.
Table 8 summarizes the properties of UST bond portfolio interest rate risk exposure measures
using monthly data from 1996 to 2018. We consider two dimensions of the bond maturity compo-
sition – pure maturity and the effect of an increasing cash share while holding the remaining share’s
maturity constant. Panel A summarizes results for maturity and Panel B summarizes results relat-
ing to varying cash share. To explore the variation in interest rate risk exposure inferences from
different return measures, we use three return measures. The first return measure is the market
return, which is calculated as the change in the value of the portfolio from period t− 1 to t. The
second measure relies on interest income returns, calculated as the income on the portfolio divided
by the beginning of period par (or book) value of portfolio. To make our results comparable to
the primary measure used in the literature, the third measure is based on interest income spreads,
with the spread calculated as the difference between the Federal funds rate (FFR) and the interest
income return as defined above.
A model-based measure of duration risk (denoted as Delta) measures the change in the value
of a bond portfolio with an increase in interest rates. It is calculated by repricing bonds after a
hypothetical 1% increase in all UST bond yields and then determining the percentage change in
value. Panel A in Table 1 clearly shows that duration risk (Delta) is increasing in the maturity of
the portfolio. The value of portfolios with a maturity or repricing date of at least 15+ years falls
by 12%, while the value of portfolios with a maturity between three months and 12 months falls
by only 1% with an increase in the interest rate. Consistent with this conceptual relation, when
we regress the various UST portfolio market returns in excess of the one-month UST yield on the
excess returns of a 5-year TERM factor, calculated as the excess return of the 5-year constant ma-
turity UST bond return series from WRDS, we find that the coefficient on the 5-year TERM factor
increases with the maturity of the portfolio, consistent with a strong relation between maturity and
TERM risk exposure.
A reliable prediction from standard asset pricing theory is that higher risk exposures are asso-
ciated with a higher risk premium. Consistent with this prediction, UST portfolios with a longer
51
maturity earn a higher mean returns than UST portfolios of shorter maturity. The mean market
return of a UST portfolio with a maturity of less than three months is 2.43% per annum, while
a portfolio with a maturity of more than 15 years has earned 7.07% on average over our sample
period. As Fama (2006) emphasizes, TERM exposure has been a highly attractive risk premium
since 1981.
Interest rate sensitivity measures based on interest income returns suggest very different prop-
erties of bond portfolio interest rate risk. Consistent with earning a higher risk premium, longer
maturity UST portfolios earn a higher mean income returns than shorter maturity bond portfo-
lios. Table 1 also shows that the volatility of interest income returns on UST portfolios decreases
with maturity. This counterfactually suggests a lower interest rate risk exposure of portfolios with
longer maturity. When we calculate interest rate risk exposures based on the change in income
returns regressed on the change in the Federal funds rate and four quarterly lags, the coefficients
decline with maturity of the UST portfolio. In addition, for portfolios with a maturity of more than
five-years, the explanatory power declines to zero.
The reason for this pattern is that the fixed income (i.e., the coupon payments) on these port-
folios sums coupons of bonds issued at different points in time. The longer the maturity, the more
coupons payments from different points in time are included in the sum and the resulting income
time series is smoother than from a shorter maturity portfolio. Figure 1, which displays the in-
come return on different bond portfolios with various maturities, shows this clearly. The longer
the maturity of the portfolio the smoother the income return. This explains why a regression of
a long-maturity bond portfolio income return on changes in the Federal funds rate will deliver a
small coefficient and little explanatory power. Figure 1 also illustrates that the mean income return
tends to be increasing in portfolio maturity, which will provide the basis for some future analyses.
Another version of the previous regression is based on the interest income spread, i.e., the
difference in the Federal funds rate and the income return. This version is more commonly used in
the recent literature (e.g., see (Drechsler, Savov, and Schnabl, 2021))) and measures the partial rate
adjustments. The coefficients on the change in the Federal funds are equal to 1 minus the coefficient
52
on the equivalent regression coefficient in the income return regression discussed above. As a
result, the coefficients, also commonly called spread betas, are now increasing with the maturity
and appear to have high explanatory power. Note though that for long maturity UST portfolios,
the variation of the dependent variable is almost exclusively coming from the Federal funds rate,
which also shows up on the right-hand side of the regression as the explanatory variable, leading
to a high R2. Higher income spread coefficients (referred to as spread betas by (Drechsler, Savov,
and Schnabl, 2017, 2021)) are interpreted as these portfolios having higher partial rate adjustment
in response to changes in market rates. It is important to note that the artificial smoothing of
interest income returns caused by the increased maturity does not translate into lower duration
risk, and of course, does not reflect a managerial action to "sluggishly" adjust rates in response
to changes in market rates. To highlight the role of the cash share ωt , we vary the cash share
from 0% to 100% for a portfolio with its remaining share invested in UST bonds of maturities
from three years to five years, results in Panel B of Table 8. Market returns and duration risk
exposure, as measured by both delta and the 5-year TERM coefficient, are declining as the cash
share increases. The average interest income return is also declining with the cash share, while
its volatility is increasing. Importantly, in regressions of the income return the coefficient on the
change in the Federal funds rate is increasing with the cash share, consistent with the premise that
this coefficient will be strongly related to the the share of (within a year with lags) zero-duration
assets in the portfolio. Equivalently, the income spread regressions have coefficients (i.e. spread
betas) that are decreasing in the cash share, which would commonly be interpreted as a decrease in
the sluggishness in rate adjustment to changes in market rates, despite these clearly being passive
portfolio strategies with no such intent.
These results demonstrate that a wide range of duration risks can be created across portfo-
lios that have different combinations of maturity and cash shares and that inferences about these
portfolio duration risk exposures will be difficult to identify with income or income spread based
measures.
To illustrate how poorly identified duration risk is with income return based measures, we con-
53
sider six portfolios strategies that seek to increase their portfolio duration risk exposure, while
maintaining a target spread beta of 0.5, by investing in constant maturity UST bonds and cash.
Table 2 reports the results from this exercise. Table 2 shows that estimated spread betas are essen-
tially constant at their specified target of 0.5, while duration risk as measured by the loading on
the 5-year Term factor more than doubles from the lowest to the highest of the considered strate-
gies. To construct this table, we calculate bond portfolios that buy bonds at maturity H and sell
them when the remaining maturity goes to h. Moving down the rows of Table 2, both the duration
risk as measured by the 5-year TERM factor as well as the cash share of the portfolio increases.
Consistent with the portfolio duration risk exposure increasing across these portfolios, the mean
returns are also monotonically increasing across these portfolios. Yet the spread beta coefficient
remains constant, demonstrating that spread betas are not informative about the extent of duration
risk exposure.
To summarize, our UST bond analysis has shown that stable income streams generated by fixed
income portfolios do not easily reveal their duration risk exposure with methods that provide the
basis for the conclusion that banks do not bear interest rate risk. Thus, these conclusions seem
premature. Empirical measures of the in the adjustment of income returns to changes in market
rates are strongly related to the maturity composition of passive UST bond portfolios.
54
Table 8: Properties of UST Portfolio IRE Measures by Maturity
0-3m 3m-12m 1y-3y 3y-5y 5y-15y 15y+
Market ReturnsMean 2.32 2.74 3.70 5.92 6.85 8.50
Std 1.09 1.24 2.20 5.91 8.06 11.20Delta 0.00 -0.01 -0.02 -0.06 -0.09 -0.12
5y-TERM Coef 0.01 0.07 0.35 1.20 1.58 2.035y-TERM t-stat (3.41) (8.67) (18.18) (26.39) (20.19) (14.60)
5y-TERM R2 0.10 0.42 0.76 0.87 0.80 0.68
Income RatesMean 2.33 2.60 3.13 4.51 5.04 4.83
Std 1.08 1.09 1.01 0.82 0.80 0.80chgFFR Coef 0.93 0.81 0.46 0.03 0.00 0.01chgFFR t-stat (29.30) (26.89) (14.19) (3.43) (0.36) (1.02)
chgFFR R2 0.92 0.90 0.68 0.10 -0.01 0.02
Interest Rate Spreads (FFR - Inc Rate)Mean 0.10 -0.18 -0.71 -2.09 -2.62 -2.41
Std 0.09 0.19 0.49 0.73 0.74 0.74chgSpread Coef 0.07 0.19 0.54 0.97 1.00 0.99chgSpread tstat (2.23) (6.29) (16.62) (100.87) (172.59) (75.79)chgSpread R2 0.48 0.82 0.91 0.99 1.00 0.99
Notes: This table reports summary statistics for various portfolios comprised of US Treasury (UST) bonds. Theconstant maturity UST portfolio invests each month in a H−period US Treasury bond and liquidates the bond whenthe maturity has reached h-periods until maturity, denoted in the headings in the format (h−H). UST portfolio marketreturns are calculated by repricing all of the bonds in the portfolio each quarter based on the current UST yield curveand the bond coupon and maturity terms. UST portfolio interest income returns are calculated based on hold-to-maturity accounting whereby the periodic portfolio value for each holding is measured at historical cost and periodiccash flows are generated by the interest payments and eventual sale proceeds or repayment of the holdings. Deltais calculated by repricing bonds after a hypothetical 1% increase in all UST bond yields and then determining thepercentage change in value. Market returns in excess of the one-month UST yield are regressed on the excess returnsof a 5-year TERM factor, calculated from the 5-year constant maturity UST bond return series from WRDS. Interestincome return regressions have the change in interest income return as the dependent variable and have the change inthe Federal funds rate (FFR) and four quarterly lags as independent variables. Interest income spreads are measuredas the FFR minus the interest income return. Changes in interest income spreads are regressed on the change in FFRwith four lags.
55
Table 9: Properties of UST Portfolio IRE Measures by Cash Share
0-3m 3m-12m 1y-3y 3y-5y 5y-15y 15y+
Market ReturnsMean 2.32 2.74 3.70 5.92 6.85 8.50
Std 1.09 1.24 2.20 5.91 8.06 11.20Delta 0.00 -0.01 -0.02 -0.06 -0.09 -0.12
5y-TERM Coef 0.01 0.07 0.35 1.20 1.58 2.035y-TERM t-stat (3.41) (8.67) (18.18) (26.39) (20.19) (14.60)
5y-TERM R2 0.10 0.42 0.76 0.87 0.80 0.68
Income RatesMean 2.33 2.60 3.13 4.51 5.04 4.83
Std 1.08 1.09 1.01 0.82 0.80 0.80chgFFR Coef 0.93 0.81 0.46 0.03 0.00 0.01chgFFR t-stat (29.30) (26.89) (14.19) (3.43) (0.36) (1.02)
chgFFR R2 0.92 0.90 0.68 0.10 -0.01 0.02
Interest Rate Spreads (FFR - Inc Rate)Mean 0.10 -0.18 -0.71 -2.09 -2.62 -2.41
Std 0.09 0.19 0.49 0.73 0.74 0.74chgSpread Coef 0.07 0.19 0.54 0.97 1.00 0.99chgSpread tstat (2.23) (6.29) (16.62) (100.87) (172.59) (75.79)chgSpread R2 0.48 0.82 0.91 0.99 1.00 0.99
Notes: This table reports summary statistics for various portfolios comprised of US Treasury (UST) bonds. Theconstant maturity UST portfolio invests each month a fraction ω in cash denoted in the headings, and 1−ω into a5-year US Treasury bond and liquidates the bond when the maturity has reached 3-years until maturity. UST portfoliomarket returns are calculated by repricing all of the bonds in the portfolio each quarter based on the current USTyield curve and the bond coupon and maturity terms. UST portfolio interest income returns are calculated based onhold-to-maturity accounting whereby the periodic portfolio value for each holding is measured at historical cost andperiodic cash flows are generated by the interest payments and eventual sale proceeds or repayment of the holdings.Delta is calculated by repricing bonds after a hypothetical 1% increase in all UST bond yields and then determining thepercentage change in value. Market returns in excess of the one-month UST yield are regressed on the excess returnsof a 5-year TERM factor, calculated from the 5-year constant maturity UST bond return series from WRDS. Interestincome return regressions have the change in interest income return as the dependent variable and have the change inthe Federal funds rate (FFR) and four quarterly lags as independent variables. Interest income spreads are measuredas the FFR minus the interest income return. Changes in interest income spreads are regressed on the change in FFRwith four lags.
56